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-Dominant- [34]
2 years ago
5

In 2006, 95% of new cars in the US came with a spare tire. In 2017, 72% came with a spare tire.

Mathematics
1 answer:
MArishka [77]2 years ago
7 0

Using the Central Limit Theorem, it is found that:

  • The mean is 0.23.
  • The standard deviation is s = \sqrt{\frac{0.95(0.05)}{250} + \frac{0.72(0.28)}{250}}.

<h3>Central Limit Theorem</h3>
  • It states that for a <u>proportion p in a sample of size n</u>, the sampling distribution of sample proportions has mean p and standard deviation s = \sqrt{\frac{p(1 - p)}{n}}
  • When two variables are subtracted, the mean is the subtraction of the means, while the standard deviation is the square root of the sum of the variances.

In 2006, 95% of new cars in the US came with a spare tire, with a sample of 250, hence:

p_1 = 0.95, s_1 = \sqrt{\frac{0.95(0.05)}{250}}

In 2017, 72% of new cars in the US came with a spare tire, with a sample of 250, hence:

p_2 = 0.72, s_2 = \sqrt{\frac{0.72(0.28)}{250}}

Hence, for the distribution of differences:

p = p_1 - p_2 = 0.95 - 0.72 = 0.23

s = \sqrt{s_1^2 + s_2^2} = \sqrt{\frac{0.95(0.05)}{250} + \frac{0.72(0.28)}{250}}

To learn more about the Central Limit Theorem, you can take a look at brainly.com/question/16695444

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Whitepunk [10]

Given the expression,

(8x-56x^2)/(\sqrt{14x-2})

We will have to rationalize the denominator first. To rationalize the denominator we have to multiply the numerator and denominator both by the square root part of the denominator.

[(8x-56x^2)(\sqrt{14x-2})]/[(\sqrt{14x-2})(\sqrt{14x-2})]

If we have (\sqrt{a})(\sqrt{a}), we will get \sqrt{a^2} by multiplying them. And \sqrt{a^2} = a.

So here in the problem, we will get,

[(8x-56x^2)(\sqrt{14x-2})]/(14x-2)

Now in the numerator we have (8x-56x^2). We can check 8x is common there. we will take out -8x from it, we will get,

-8x(-1+7x)

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And in the denominator we have 14x-2. We can check 2 is common there. If we take out 2 from it we will get,

2(7x-1)

So we can write the expression as

[(-8x)(7x-1)(\sqrt{14x-2})]/[2(7x-1)]

(7x-1) is common to the numerator and denominator both, if we cancel it we will get,

(-8x)(\sqrt{14x-2})/2

We can divide -8 by the denominator, as -8 os divisible by 2. By dividing them we will get,

(-4x)(\sqrt{14x-2})

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So we have got the required answer here.

The correct option is the last one.

4 0
3 years ago
Emily has 300 books. if frank were to double the number of books that he now owns, he would still have fewer than Emily has
Alex_Xolod [135]
This statement is false. 
If he were to double the amount that Emily has to get franks, franks would have more. 
Look :)
Emily's = 300
Frank's = 300 x 2 = 600

now...
Emily's = 300
Frank's = 600

So frank has more! NOT fewer. 

8 0
3 years ago
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DerKrebs [107]

Answer:

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The probability of rolling at least one six is therefore 1 − 625/1296 = 671/1296 ≈ . 517.

Step-by-step explanation:

4 0
3 years ago
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egoroff_w [7]
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3(m-5)+m

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The answer is A!

Hope that helps

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